Problem: Express your answer as a mixed number simplified to lowest terms. $9\dfrac{1}{6}-6\dfrac{2}{4} = {?}$
Answer: Simplify each fraction. $= {9\dfrac{1}{6}} - {6\dfrac{1}{2}}$ Find a common denominator for the fractions: $= {9\dfrac{1}{6}}-{6\dfrac{3}{6}}$ Convert ${9\dfrac{1}{6}}$ to ${8 + \dfrac{6}{6} + \dfrac{1}{6}}$ So the problem becomes: ${8\dfrac{7}{6}}-{6\dfrac{3}{6}}$ Separate the whole numbers from the fractional parts: $= {8} + {\dfrac{7}{6}} - {6} - {\dfrac{3}{6}}$ Bring the whole numbers together and the fractions together: $= {8} - {6} + {\dfrac{7}{6}} - {\dfrac{3}{6}}$ Subtract the whole numbers: $=2 + {\dfrac{7}{6}} - {\dfrac{3}{6}}$ Subtract the fractions: $= 2+\dfrac{4}{6}$ Combine the whole and fractional parts into a mixed number: $= 2\dfrac{4}{6}$ Simplify to lowest terms: $= 2\dfrac{2}{3}$